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BatchLinearAlgebra.cpp
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BatchLinearAlgebra.cpp
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#include <ATen/ATen.h>
#include <ATen/CPUApplyUtils.h>
#include <ATen/Dispatch.h>
#include <ATen/NativeFunctions.h>
#include <ATen/ExpandUtils.h>
#include <ATen/native/BatchLinearAlgebra.h>
#include <ATen/native/LinearAlgebraUtils.h>
#include <ATen/native/Resize.h>
#include <ATen/native/cpu/zmath.h>
#include <ATen/Parallel.h>
#include <TH/TH.h> // for USE_LAPACK
#include <vector>
// First the required LAPACK implementations are registered here.
// A comment above the registered LAPACK routine suggest which batched
// linear algebra function uses that routine
#ifdef USE_LAPACK
// gesv
extern "C" void zgesv_(int *n, int *nrhs, std::complex<double> *a, int *lda, int *ipiv, std::complex<double> *b, int *ldb, int *info);
extern "C" void cgesv_(int *n, int *nrhs, std::complex<float> *a, int *lda, int *ipiv, std::complex<float> *b, int *ldb, int *info);
extern "C" void dgesv_(int *n, int *nrhs, double *a, int *lda, int *ipiv, double *b, int *ldb, int *info);
extern "C" void sgesv_(int *n, int *nrhs, float *a, int *lda, int *ipiv, float *b, int *ldb, int *info);
// getrf
extern "C" void zgetrf_(int *m, int *n, std::complex<double> *a, int *lda, int *ipiv, int *info);
extern "C" void cgetrf_(int *m, int *n, std::complex<float> *a, int *lda, int *ipiv, int *info);
extern "C" void dgetrf_(int *m, int *n, double *a, int *lda, int *ipiv, int *info);
extern "C" void sgetrf_(int *m, int *n, float *a, int *lda, int *ipiv, int *info);
// getri
extern "C" void zgetri_(int *n, std::complex<double> *a, int *lda, int *ipiv, std::complex<double> *work, int *lwork, int *info);
extern "C" void cgetri_(int *n, std::complex<float> *a, int *lda, int *ipiv, std::complex<float> *work, int *lwork, int *info);
extern "C" void dgetri_(int *n, double *a, int *lda, int *ipiv, double *work, int *lwork, int *info);
extern "C" void sgetri_(int *n, float *a, int *lda, int *ipiv, float *work, int *lwork, int *info);
// potrs
extern "C" void zpotrs_(char *uplo, int *n, int *nrhs, std::complex<double> *a, int *lda, std::complex<double> *b, int *ldb, int *info);
extern "C" void cpotrs_(char *uplo, int *n, int *nrhs, std::complex<float> *a, int *lda, std::complex<float> *b, int *ldb, int *info);
extern "C" void dpotrs_(char *uplo, int *n, int *nrhs, double *a, int *lda, double *b, int *ldb, int *info);
extern "C" void spotrs_(char *uplo, int *n, int *nrhs, float *a, int *lda, float *b, int *ldb, int *info);
// potrf
extern "C" void zpotrf_(char *uplo, int *n, std::complex<double> *a, int *lda, int *info);
extern "C" void cpotrf_(char *uplo, int *n, std::complex<float> *a, int *lda, int *info);
extern "C" void dpotrf_(char *uplo, int *n, double *a, int *lda, int *info);
extern "C" void spotrf_(char *uplo, int *n, float *a, int *lda, int *info);
// trtrs
extern "C" void ztrtrs_(char *uplo, char *trans, char *diag, int *n, int *nrhs, std::complex<double> *a, int *lda, std::complex<double> *b, int *ldb, int *info);
extern "C" void ctrtrs_(char *uplo, char *trans, char *diag, int *n, int *nrhs, std::complex<float> *a, int *lda, std::complex<float> *b, int *ldb, int *info);
extern "C" void dtrtrs_(char *uplo, char *trans, char *diag, int *n, int *nrhs, double *a, int *lda, double *b, int *ldb, int *info);
extern "C" void strtrs_(char *uplo, char *trans, char *diag, int *n, int *nrhs, float *a, int *lda, float *b, int *ldb, int *info);
// geqrf
extern "C" void zgeqrf_(int *m, int *n, std::complex<double> *a, int *lda, std::complex<double> *tau, std::complex<double> *work, int *lwork, int *info);
extern "C" void cgeqrf_(int *m, int *n, std::complex<float> *a, int *lda, std::complex<float> *tau, std::complex<float> *work, int *lwork, int *info);
extern "C" void dgeqrf_(int *m, int *n, double *a, int *lda, double *tau, double *work, int *lwork, int *info);
extern "C" void sgeqrf_(int *m, int *n, float *a, int *lda, float *tau, float *work, int *lwork, int *info);
// orgqr
extern "C" void zungqr_(int *m, int *n, int *k, std::complex<double> *a, int *lda, std::complex<double> *tau, std::complex<double> *work, int *lwork, int *info);
extern "C" void cungqr_(int *m, int *n, int *k, std::complex<float> *a, int *lda, std::complex<float> *tau, std::complex<float> *work, int *lwork, int *info);
extern "C" void dorgqr_(int *m, int *n, int *k, double *a, int *lda, double *tau, double *work, int *lwork, int *info);
extern "C" void sorgqr_(int *m, int *n, int *k, float *a, int *lda, float *tau, float *work, int *lwork, int *info);
// syev
extern "C" void zheev_(char *jobz, char *uplo, int *n, std::complex<double> *a, int *lda, double *w, std::complex<double> *work, int *lwork, double *rwork, int *info);
extern "C" void cheev_(char *jobz, char *uplo, int *n, std::complex<float> *a, int *lda, float *w, std::complex<float> *work, int *lwork, float *rwork, int *info);
extern "C" void dsyev_(char *jobz, char *uplo, int *n, double *a, int *lda, double *w, double *work, int *lwork, int *info);
extern "C" void ssyev_(char *jobz, char *uplo, int *n, float *a, int *lda, float *w, float *work, int *lwork, int *info);
// syevd
extern "C" void zheevd_(char *jobz, char *uplo, int *n, std::complex<double> *a, int *lda, double *w, std::complex<double> *work, int *lwork, double *rwork, int *lrwork, int *iwork, int *liwork, int *info);
extern "C" void cheevd_(char *jobz, char *uplo, int *n, std::complex<float> *a, int *lda, float *w, std::complex<float> *work, int *lwork, float *rwork, int *lrwork, int *iwork, int *liwork, int *info);
extern "C" void dsyevd_(char *jobz, char *uplo, int *n, double *a, int *lda, double *w, double *work, int *lwork, int *iwork, int *liwork, int *info);
extern "C" void ssyevd_(char *jobz, char *uplo, int *n, float *a, int *lda, float *w, float *work, int *lwork, int *iwork, int *liwork, int *info);
// geev
extern "C" void dgeev_(char *jobvl, char *jobvr, int *n, double *a, int *lda, double *wr, double *wi, double* vl, int *ldvl, double *vr, int *ldvr, double *work, int *lwork, int *info);
extern "C" void sgeev_(char *jobvl, char *jobvr, int *n, float *a, int *lda, float *wr, float *wi, float* vl, int *ldvl, float *vr, int *ldvr, float *work, int *lwork, int *info);
// gesdd
extern "C" void zgesdd_(char *jobz, int *m, int *n, std::complex<double> *a, int *lda,
double *s, std::complex<double> *u, int *ldu, std::complex<double> *vt, int *ldvt, std::complex<double> *work, int *lwork, double *rwork, int *iwork, int *info);
extern "C" void cgesdd_(char *jobz, int *m, int *n, std::complex<float> *a, int *lda,
float *s, std::complex<float> *u, int *ldu, std::complex<float> *vt, int *ldvt, std::complex<float> *work, int *lwork, float *rwork, int *iwork, int *info);
extern "C" void dgesdd_(char *jobz, int *m, int *n, double *a, int *lda,
double *s, double *u, int *ldu, double *vt, int *ldvt, double *work, int *lwork, int *iwork, int *info);
extern "C" void sgesdd_(char *jobz, int *m, int *n, float *a, int *lda,
float *s, float *u, int *ldu, float *vt, int *ldvt, float *work, int *lwork, int *iwork, int *info);
// getrs
extern "C" void zgetrs_(char *trans, int *n, int *nrhs, std::complex<double> *a, int *lda, int *ipiv, std::complex<double> *b, int *ldb, int *info);
extern "C" void cgetrs_(char *trans, int *n, int *nrhs, std::complex<float> *a, int *lda, int *ipiv, std::complex<float> *b, int *ldb, int *info);
extern "C" void dgetrs_(char *trans, int *n, int *nrhs, double *a, int *lda, int *ipiv, double *b, int *ldb, int *info);
extern "C" void sgetrs_(char *trans, int *n, int *nrhs, float *a, int *lda, int *ipiv, float *b, int *ldb, int *info);
#endif
namespace at {
namespace native {
#ifdef USE_LAPACK
// Define the per-batch functions to be used in the main implementation of the batched
// linear algebra operations
template<class scalar_t>
void lapackSolve(int n, int nrhs, scalar_t *a, int lda, int *ipiv, scalar_t *b, int ldb, int *info);
template<class scalar_t>
void lapackLu(int m, int n, scalar_t *a, int lda, int *ipiv, int *info);
template<class scalar_t>
void lapackGetri(int n, scalar_t *a, int lda, int *ipiv, scalar_t *work, int lwork, int *info);
template<class scalar_t>
void lapackCholeskySolve(char uplo, int n, int nrhs, scalar_t *a, int lda, scalar_t *b, int ldb, int *info);
template<class scalar_t>
void lapackCholesky(char uplo, int n, scalar_t *a, int lda, int *info);
template<class scalar_t>
void lapackTriangularSolve(char uplo, char trans, char diag, int n, int nrhs, scalar_t *a, int lda, scalar_t *b, int ldb, int *info);
template<class scalar_t>
void lapackGeqrf(int m, int n, scalar_t *a, int lda, scalar_t *tau, scalar_t *work, int lwork, int *info);
template<class scalar_t>
void lapackOrgqr(int m, int n, int k, scalar_t *a, int lda, scalar_t *tau, scalar_t *work, int lwork, int *info);
template<class scalar_t, class value_t=scalar_t>
void lapackSymeig(char jobz, char uplo, int n, scalar_t *a, int lda, value_t *w, scalar_t *work, int lwork, value_t *rwork, int *info);
template<class scalar_t, class value_t=scalar_t>
void lapackSyevd(char jobz, char uplo, int n, scalar_t *a, int lda, value_t *w, scalar_t *work, int lwork, value_t *rwork, int lrwork, int *iwork, int liwork, int *info);
template<class scalar_t, class value_t=scalar_t>
void lapackSvd(char jobz, int m, int n, scalar_t *a, int lda,
value_t *s, scalar_t *u, int ldu, scalar_t *vt, int ldvt, scalar_t *work, int lwork, value_t *rwork, int *iwork, int *info);
template<class scalar_t>
void lapackLuSolve(char trans, int n, int nrhs, scalar_t *a, int lda, int *ipiv, scalar_t *b, int ldb, int *info);
template<> void lapackSolve<c10::complex<double>>(int n, int nrhs, c10::complex<double> *a, int lda, int *ipiv, c10::complex<double> *b, int ldb, int *info) {
zgesv_(&n, &nrhs, reinterpret_cast<std::complex<double>*>(a), &lda, ipiv, reinterpret_cast<std::complex<double>*>(b), &ldb, info);
}
template<> void lapackSolve<c10::complex<float>>(int n, int nrhs, c10::complex<float> *a, int lda, int *ipiv, c10::complex<float> *b, int ldb, int *info) {
cgesv_(&n, &nrhs, reinterpret_cast<std::complex<float>*>(a), &lda, ipiv, reinterpret_cast<std::complex<float>*>(b), &ldb, info);
}
template<> void lapackSolve<double>(int n, int nrhs, double *a, int lda, int *ipiv, double *b, int ldb, int *info) {
dgesv_(&n, &nrhs, a, &lda, ipiv, b, &ldb, info);
}
template<> void lapackSolve<float>(int n, int nrhs, float *a, int lda, int *ipiv, float *b, int ldb, int *info) {
sgesv_(&n, &nrhs, a, &lda, ipiv, b, &ldb, info);
}
template<> void lapackGetri<c10::complex<double>>(int n, c10::complex<double> *a, int lda, int *ipiv, c10::complex<double> *work, int lwork, int *info) {
zgetri_(&n, reinterpret_cast<std::complex<double>*>(a), &lda, ipiv, reinterpret_cast<std::complex<double>*>(work), &lwork, info);
}
template<> void lapackGetri<c10::complex<float>>(int n, c10::complex<float> *a, int lda, int *ipiv, c10::complex<float> *work, int lwork, int *info) {
cgetri_(&n, reinterpret_cast<std::complex<float>*>(a), &lda, ipiv, reinterpret_cast<std::complex<float>*>(work), &lwork, info);
}
template<> void lapackGetri<double>(int n, double *a, int lda, int *ipiv, double *work, int lwork, int *info) {
dgetri_(&n, a, &lda, ipiv, work, &lwork, info);
}
template<> void lapackGetri<float>(int n, float *a, int lda, int *ipiv, float *work, int lwork, int *info) {
sgetri_(&n, a, &lda, ipiv, work, &lwork, info);
}
template<> void lapackLu<c10::complex<double>>(int m, int n, c10::complex<double> *a, int lda, int *ipiv, int *info) {
zgetrf_(&m, &n, reinterpret_cast<std::complex<double>*>(a), &lda, ipiv, info);
}
template<> void lapackLu<c10::complex<float>>(int m, int n, c10::complex<float> *a, int lda, int *ipiv, int *info) {
cgetrf_(&m, &n, reinterpret_cast<std::complex<float>*>(a), &lda, ipiv, info);
}
template<> void lapackLu<double>(int m, int n, double *a, int lda, int *ipiv, int *info) {
dgetrf_(&m, &n, a, &lda, ipiv, info);
}
template<> void lapackLu<float>(int m, int n, float *a, int lda, int *ipiv, int *info) {
sgetrf_(&m, &n, a, &lda, ipiv, info);
}
template<> void lapackCholeskySolve<c10::complex<double>>(char uplo, int n, int nrhs, c10::complex<double> *a, int lda, c10::complex<double> *b, int ldb, int *info) {
zpotrs_(&uplo, &n, &nrhs, reinterpret_cast<std::complex<double>*>(a), &lda, reinterpret_cast<std::complex<double>*>(b), &ldb, info);
}
template<> void lapackCholeskySolve<c10::complex<float>>(char uplo, int n, int nrhs, c10::complex<float> *a, int lda, c10::complex<float> *b, int ldb, int *info) {
cpotrs_(&uplo, &n, &nrhs, reinterpret_cast<std::complex<float>*>(a), &lda, reinterpret_cast<std::complex<float>*>(b), &ldb, info);
}
template<> void lapackCholeskySolve<double>(char uplo, int n, int nrhs, double *a, int lda, double *b, int ldb, int *info) {
dpotrs_(&uplo, &n, &nrhs, a, &lda, b, &ldb, info);
}
template<> void lapackCholeskySolve<float>(char uplo, int n, int nrhs, float *a, int lda, float *b, int ldb, int *info) {
spotrs_(&uplo, &n, &nrhs, a, &lda, b, &ldb, info);
}
template<> void lapackCholesky<c10::complex<double>>(char uplo, int n, c10::complex<double> *a, int lda, int *info) {
zpotrf_(&uplo, &n, reinterpret_cast<std::complex<double>*>(a), &lda, info);
}
template<> void lapackCholesky<c10::complex<float>>(char uplo, int n, c10::complex<float> *a, int lda, int *info) {
cpotrf_(&uplo, &n, reinterpret_cast<std::complex<float>*>(a), &lda, info);
}
template<> void lapackCholesky<double>(char uplo, int n, double *a, int lda, int *info) {
dpotrf_(&uplo, &n, a, &lda, info);
}
template<> void lapackCholesky<float>(char uplo, int n, float *a, int lda, int *info) {
spotrf_(&uplo, &n, a, &lda, info);
}
template<> void lapackTriangularSolve<c10::complex<double>>(char uplo, char trans, char diag, int n, int nrhs, c10::complex<double> *a, int lda, c10::complex<double> *b, int ldb, int *info) {
ztrtrs_(&uplo, &trans, &diag, &n, &nrhs, reinterpret_cast<std::complex<double>*>(a), &lda, reinterpret_cast<std::complex<double>*>(b), &ldb, info);
}
template<> void lapackTriangularSolve<c10::complex<float>>(char uplo, char trans, char diag, int n, int nrhs, c10::complex<float> *a, int lda, c10::complex<float> *b, int ldb, int *info) {
ctrtrs_(&uplo, &trans, &diag, &n, &nrhs, reinterpret_cast<std::complex<float>*>(a), &lda, reinterpret_cast<std::complex<float>*>(b), &ldb, info);
}
template<> void lapackTriangularSolve<double>(char uplo, char trans, char diag, int n, int nrhs, double *a, int lda, double *b, int ldb, int *info) {
dtrtrs_(&uplo, &trans, &diag, &n, &nrhs, a, &lda, b, &ldb, info);
}
template<> void lapackTriangularSolve<float>(char uplo, char trans, char diag, int n, int nrhs, float *a, int lda, float *b, int ldb, int *info) {
strtrs_(&uplo, &trans, &diag, &n, &nrhs, a, &lda, b, &ldb, info);
}
template<> void lapackGeqrf<c10::complex<double>>(int m, int n, c10::complex<double> *a, int lda, c10::complex<double> *tau, c10::complex<double> *work, int lwork, int *info) {
zgeqrf_(&m, &n, reinterpret_cast<std::complex<double>*>(a), &lda, reinterpret_cast<std::complex<double>*>(tau), reinterpret_cast<std::complex<double>*>(work), &lwork, info);
}
template<> void lapackGeqrf<c10::complex<float>>(int m, int n, c10::complex<float> *a, int lda, c10::complex<float> *tau, c10::complex<float> *work, int lwork, int *info) {
cgeqrf_(&m, &n, reinterpret_cast<std::complex<float>*>(a), &lda, reinterpret_cast<std::complex<float>*>(tau), reinterpret_cast<std::complex<float>*>(work), &lwork, info);
}
template<> void lapackGeqrf<double>(int m, int n, double *a, int lda, double *tau, double *work, int lwork, int *info) {
dgeqrf_(&m, &n, a, &lda, tau, work, &lwork, info);
}
template<> void lapackGeqrf<float>(int m, int n, float *a, int lda, float *tau, float *work, int lwork, int *info) {
sgeqrf_(&m, &n, a, &lda, tau, work, &lwork, info);
}
template<> void lapackOrgqr<c10::complex<double>>(int m, int n, int k, c10::complex<double> *a, int lda, c10::complex<double> *tau, c10::complex<double> *work, int lwork, int *info) {
zungqr_(&m, &n, &k, reinterpret_cast<std::complex<double>*>(a), &lda, reinterpret_cast<std::complex<double>*>(tau), reinterpret_cast<std::complex<double>*>(work), &lwork, info);
}
template<> void lapackOrgqr<c10::complex<float>>(int m, int n, int k, c10::complex<float> *a, int lda, c10::complex<float> *tau, c10::complex<float> *work, int lwork, int *info) {
cungqr_(&m, &n, &k, reinterpret_cast<std::complex<float>*>(a), &lda, reinterpret_cast<std::complex<float>*>(tau), reinterpret_cast<std::complex<float>*>(work), &lwork, info);
}
template<> void lapackOrgqr<double>(int m, int n, int k, double *a, int lda, double *tau, double *work, int lwork, int *info) {
dorgqr_(&m, &n, &k, a, &lda, tau, work, &lwork, info);
}
template<> void lapackOrgqr<float>(int m, int n, int k, float *a, int lda, float *tau, float *work, int lwork, int *info) {
sorgqr_(&m, &n, &k, a, &lda, tau, work, &lwork, info);
}
template<> void lapackSymeig<c10::complex<double>, double>(char jobz, char uplo, int n, c10::complex<double> *a, int lda, double *w, c10::complex<double> *work, int lwork, double *rwork, int *info) {
zheev_(&jobz, &uplo, &n, reinterpret_cast<std::complex<double>*>(a), &lda, w, reinterpret_cast<std::complex<double>*>(work), &lwork, rwork, info);
}
template<> void lapackSymeig<c10::complex<float>, float>(char jobz, char uplo, int n, c10::complex<float> *a, int lda, float *w, c10::complex<float> *work, int lwork, float *rwork, int *info) {
cheev_(&jobz, &uplo, &n, reinterpret_cast<std::complex<float>*>(a), &lda, w, reinterpret_cast<std::complex<float>*>(work), &lwork, rwork, info);
}
template<> void lapackSymeig<double>(char jobz, char uplo, int n, double *a, int lda, double *w, double *work, int lwork, double* rwork, int *info) {
(void)rwork; // unused
dsyev_(&jobz, &uplo, &n, a, &lda, w, work, &lwork, info);
}
template<> void lapackSymeig<float>(char jobz, char uplo, int n, float *a, int lda, float *w, float *work, int lwork, float* rwork, int *info) {
(void)rwork; // unused
ssyev_(&jobz, &uplo, &n, a, &lda, w, work, &lwork, info);
}
template<> void lapackSyevd<c10::complex<double>, double>(char jobz, char uplo, int n, c10::complex<double> *a, int lda, double *w, c10::complex<double> *work, int lwork, double *rwork, int lrwork, int *iwork, int liwork, int *info) {
zheevd_(&jobz, &uplo, &n, reinterpret_cast<std::complex<double>*>(a), &lda, w, reinterpret_cast<std::complex<double>*>(work), &lwork, rwork, &lrwork, iwork, &liwork, info);
}
template<> void lapackSyevd<c10::complex<float>, float>(char jobz, char uplo, int n, c10::complex<float> *a, int lda, float *w, c10::complex<float> *work, int lwork, float *rwork, int lrwork, int *iwork, int liwork, int *info) {
cheevd_(&jobz, &uplo, &n, reinterpret_cast<std::complex<float>*>(a), &lda, w, reinterpret_cast<std::complex<float>*>(work), &lwork, rwork, &lrwork, iwork, &liwork, info);
}
template<> void lapackSyevd<double>(char jobz, char uplo, int n, double *a, int lda, double *w, double *work, int lwork, double *rwork, int lrwork, int *iwork, int liwork, int *info) {
(void)rwork; // unused
(void)lrwork; // unused
dsyevd_(&jobz, &uplo, &n, a, &lda, w, work, &lwork, iwork, &liwork, info);
}
template<> void lapackSyevd<float>(char jobz, char uplo, int n, float *a, int lda, float *w, float *work, int lwork, float *rwork, int lrwork, int *iwork, int liwork, int *info) {
(void)rwork; // unused
(void)lrwork; // unused
ssyevd_(&jobz, &uplo, &n, a, &lda, w, work, &lwork, iwork, &liwork, info);
}
template<> void lapackEig<double>(char jobvl, char jobvr, int n, double *a, int lda, double *wr, double *wi, double* vl, int ldvl, double *vr, int ldvr, double *work, int lwork, int *info) {
dgeev_(&jobvl, &jobvr, &n, a, &lda, wr, wi, vl, &ldvl, vr, &ldvr, work, &lwork, info);
}
template<> void lapackEig<float>(char jobvl, char jobvr, int n, float *a, int lda, float *wr, float *wi, float* vl, int ldvl, float *vr, int ldvr, float *work, int lwork, int *info) {
sgeev_(&jobvl, &jobvr, &n, a, &lda, wr, wi, vl, &ldvl, vr, &ldvr, work, &lwork, info);
}
template<> void lapackSvd<c10::complex<double>, double>(char jobz, int m, int n, c10::complex<double> *a, int lda,
double *s, c10::complex<double> *u, int ldu, c10::complex<double> *vt, int ldvt, c10::complex<double> *work, int lwork, double *rwork, int *iwork, int *info) {
zgesdd_(&jobz, &m, &n, reinterpret_cast<std::complex<double>*>(a), &lda, s, reinterpret_cast<std::complex<double>*>(u), &ldu,
reinterpret_cast<std::complex<double>*>(vt), &ldvt, reinterpret_cast<std::complex<double>*>(work), &lwork, rwork, iwork, info);
}
template<> void lapackSvd<c10::complex<float>, float>(char jobz, int m, int n, c10::complex<float> *a, int lda,
float *s, c10::complex<float> *u, int ldu, c10::complex<float> *vt, int ldvt, c10::complex<float> *work, int lwork, float *rwork, int *iwork, int *info) {
cgesdd_(&jobz, &m, &n, reinterpret_cast<std::complex<float>*>(a), &lda, s, reinterpret_cast<std::complex<float>*>(u), &ldu,
reinterpret_cast<std::complex<float>*>(vt), &ldvt, reinterpret_cast<std::complex<float>*>(work), &lwork, rwork, iwork, info);
}
template<> void lapackSvd<double>(char jobz, int m, int n, double *a, int lda,
double *s, double *u, int ldu, double *vt, int ldvt, double *work, int lwork, double *rwork, int *iwork, int *info) {
dgesdd_(&jobz, &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, work, &lwork, iwork, info);
}
template<> void lapackSvd<float>(char jobz, int m, int n, float *a, int lda,
float *s, float *u, int ldu, float *vt, int ldvt, float *work, int lwork, float *rwork, int *iwork, int *info) {
sgesdd_(&jobz, &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, work, &lwork, iwork, info);
}
template<> void lapackLuSolve<c10::complex<double>>(char trans, int n, int nrhs, c10::complex<double> *a, int lda, int *ipiv, c10::complex<double> *b, int ldb, int *info) {
zgetrs_(&trans, &n, &nrhs, reinterpret_cast<std::complex<double>*>(a), &lda, ipiv, reinterpret_cast<std::complex<double>*>(b), &ldb, info);
}
template<> void lapackLuSolve<c10::complex<float>>(char trans, int n, int nrhs, c10::complex<float> *a, int lda, int *ipiv, c10::complex<float> *b, int ldb, int *info) {
cgetrs_(&trans, &n, &nrhs, reinterpret_cast<std::complex<float>*>(a), &lda, ipiv, reinterpret_cast<std::complex<float>*>(b), &ldb, info);
}
template<> void lapackLuSolve<double>(char trans, int n, int nrhs, double *a, int lda, int *ipiv, double *b, int ldb, int *info) {
dgetrs_(&trans, &n, &nrhs, a, &lda, ipiv, b, &ldb, info);
}
template<> void lapackLuSolve<float>(char trans, int n, int nrhs, float *a, int lda, int *ipiv, float *b, int ldb, int *info) {
sgetrs_(&trans, &n, &nrhs, a, &lda, ipiv, b, &ldb, info);
}
#endif
// Below of the definitions of the functions operating on a batch that are going to be dispatched
// in the main helper functions for the linear algebra operations
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ solve ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/*
Computes the solution to a system of linear equations
A X = B,
where A is an n-by-n matrix and X and B are n-by-nrhs matrices.
Note that B is required to be a matrix, the usual, vector case, is obtained with nrhs = 1.
Above description is for non-batched input, the batched input is also supported.
This is an in-place routine, content of both A and b are overriden.
'infos' is an int Tensor containing error codes for each matrix in the batched input.
For more information see LAPACK's documentation for GESV routine.
*/
template<typename scalar_t>
static void apply_solve(Tensor& b, Tensor& A, Tensor& infos) {
#ifndef USE_LAPACK
AT_ERROR("solve: LAPACK library not found in compilation");
#else
auto A_data = A.data_ptr<scalar_t>();
auto b_data = b.data_ptr<scalar_t>();
auto A_mat_stride = matrixStride(A);
auto b_mat_stride = matrixStride(b);
auto batch_size = batchCount(A);
auto n = A.size(-2);
auto nrhs = b.size(-1);
auto lda = std::max<int64_t>(1, n);
auto ipiv = at::empty({lda}, b.options().dtype(kInt));
auto ipiv_data = ipiv.data_ptr<int>();
auto infos_data = infos.data_ptr<int>();
for (int64_t i = 0; i < batch_size; i++) {
scalar_t* A_working_ptr = &A_data[i * A_mat_stride];
scalar_t* b_working_ptr = &b_data[i * b_mat_stride];
int* info_working_ptr = &infos_data[i];
lapackSolve<scalar_t>(n, nrhs, A_working_ptr, lda, ipiv_data, b_working_ptr, lda, info_working_ptr);
}
#endif
}
std::tuple<Tensor, Tensor> _solve_helper_cpu(const Tensor& self, const Tensor& A) {
auto self_working_copy = cloneBatchedColumnMajor(self);
auto A_working_copy = cloneBatchedColumnMajor(A);
auto infos = at::empty({std::max<int64_t>(1, batchCount(self))}, self.options().dtype(kInt));
AT_DISPATCH_FLOATING_AND_COMPLEX_TYPES(self.scalar_type(), "solve_cpu", [&]{
apply_solve<scalar_t>(self_working_copy, A_working_copy, infos);
});
if (self.dim() > 2) {
batchCheckErrors(infos, "solve_cpu");
} else {
singleCheckErrors(infos.item().toInt(), "solve_cpu");
}
return std::tuple<Tensor, Tensor>(self_working_copy, A_working_copy);
}
// Supports arbitrary batch dimensions for self and A
std::tuple<Tensor,Tensor> solve(const Tensor& self, const Tensor& A) {
TORCH_CHECK(self.dim() >= 2,
"B should have at least 2 dimensions, but has ", self.dim(), " dimensions instead");
TORCH_CHECK(A.dim() >= 2,
"A should have at least 2 dimensions, but has ", A.dim(), " dimensions instead");
Tensor self_broadcasted, A_broadcasted;
std::tie(self_broadcasted, A_broadcasted) = _linalg_broadcast_batch_dims(self, A, "solve");
return at::_solve_helper(self_broadcasted, A_broadcasted);
}
std::tuple<Tensor&,Tensor&> solve_out(Tensor& solution, Tensor& lu, const Tensor& self, const Tensor& A) {
Tensor solution_tmp, lu_tmp;
std::tie(solution_tmp, lu_tmp) = at::_solve_helper(self, A);
solution.resize_as_(solution_tmp).copy_(solution_tmp);
lu.resize_as_(lu_tmp).copy_(lu_tmp);
return std::tuple<Tensor&, Tensor&>(solution, lu);
}
// This is a type dispatching helper function for 'apply_solve'
Tensor& _linalg_solve_out_helper_cpu(Tensor& result, Tensor& input, Tensor& infos) {
// 'result' and 'input' should be in column major order (it should be checked before calling this function)
// the content of 'result', 'input' and 'infos' is overriden by 'apply_solve'
// 'result' should contain data of 'other' tensor (right-hand-side of the linear system of equations)
// 'input' should contain data of original 'input' tensor (left-hand-side of the linear system of equations)
AT_DISPATCH_FLOATING_AND_COMPLEX_TYPES(result.scalar_type(), "linalg_solve_out_cpu", [&]{
apply_solve<scalar_t>(result, input, infos);
});
return result;
}
// Solves a system of linear equations matmul(input, x) = other in-place
// LAPACK/MAGMA error codes are saved in 'infos' tensor, they are not checked here
static Tensor& linalg_solve_out_info(Tensor& result, Tensor& infos, const Tensor& input, const Tensor& other) {
TORCH_CHECK(infos.scalar_type() == kInt,
"infos dtype ", infos.scalar_type(), " does not match the expected dtype ", kInt);
TORCH_CHECK(result.scalar_type() == input.scalar_type(),
"result dtype ", result.scalar_type(), " does not match input dtype ", input.scalar_type());
TORCH_CHECK(input.scalar_type() == other.scalar_type(),
"input dtype ", input.scalar_type(), " does not match other dtype ", other.scalar_type());
TORCH_CHECK(input.dim() >= 2,
"input should have at least 2 dimensions, but has ", input.dim(), " dimensions instead");
TORCH_CHECK(other.dim() >= 1,
"other should have at least 1 dimension, but has ", other.dim(), " dimensions instead");
// NumPy works for 1-dimensional 'other' or batch of 1-dimensional tensors, we need to unsqueeze it
// because 2-dimensional tensors are expected in the implementation
auto expected_batched_rhs_shape = IntArrayRef(input.sizes().data(), input.dim()-1); // A.shape[:-1]
bool is_rhs_broadcasted = other.dim() == 1 || (input.dim()-1 == other.dim() && other.sizes().equals(expected_batched_rhs_shape));
Tensor other_ = is_rhs_broadcasted ? other.unsqueeze(-1) : other;
// _linalg_broadcast_batch_dims also includes linearSolveCheckInputs
// it checks for squareness of 'input' and 'shape' compatibility of 'other' and 'input'
Tensor other_broadcasted, input_broadcasted;
std::tie(other_broadcasted, input_broadcasted) = _linalg_broadcast_batch_dims(other_, input, "linalg_solve");
// if result has no elements we can modify it
if (result.numel() == 0) {
at::native::resize_as_(result, other_broadcasted.transpose(-2, -1), MemoryFormat::Contiguous);
result.transpose_(-2, -1);
} else {
// Resize messes up the strides and we expect strictly column major order, so let's not use at::native::resize_output
TORCH_CHECK(result.sizes().equals(other_broadcasted.sizes()),
"result shape ", result.sizes(), " does not match broadcasted other shape ", other_broadcasted.sizes());
}
TORCH_CHECK(result.transpose(-2, -1).is_contiguous(), "result tensor must be in batched column major order (Fortran contiguous).");
result.copy_(other_broadcasted);
auto input_working_copy = cloneBatchedColumnMajor(input_broadcasted);
at::native::resize_output(infos, {std::max<int64_t>(1, batchCount(input_broadcasted))});
// if input is empty infos might not get filled; make sure infos doesn't contain garbage then
if (input.numel() == 0) {
infos.fill_(0);
}
result = at::_linalg_solve_out_helper_(result, input_working_copy, infos);
// NumPy works for 1-dimensional 'other', we need to squeeze the result in this case
if (is_rhs_broadcasted) {
result.squeeze_(-1);
}
return result;
}
// Solves a system of linear equations matmul(input, x) = other in-place
Tensor& linalg_solve_out(Tensor& result, const Tensor& input, const Tensor& other) {
auto infos = at::empty({0}, input.options().dtype(kInt));
result = linalg_solve_out_info(result, infos, input, other);
// Now check LAPACK/MAGMA error codes
// batchCheckErrors(Tensor, char*) calls 'infos = infos.to(kCPU)'
auto expected_batched_rhs_shape = IntArrayRef(input.sizes().data(), input.dim()-1); // A.shape[:-1]
bool is_rhs_broadcasted = other.dim() == 1 || (input.dim()-1 == other.dim() && other.sizes().equals(expected_batched_rhs_shape));
if (is_rhs_broadcasted ? result.dim() > 1 : result.dim() > 2) {
batchCheckErrors(infos, "linalg_solve");
} else {
singleCheckErrors(infos.item().toInt(), "linalg_solve");
}
return result;
}
// Solves a system of linear equations matmul(input, x) = other
Tensor linalg_solve(const Tensor& input, const Tensor& other) {
Tensor result = at::empty({0}, input.options());
result = at::linalg_solve_out(result, input, other);
return result;
}
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ inverse ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
template <typename scalar_t>
static void apply_inverse(Tensor& self, std::vector<int64_t>& infos) {
#ifndef USE_LAPACK
AT_ERROR("inverse: LAPACK library not found in compilation");
#else
using value_t = typename c10::scalar_value_type<scalar_t>::type;
auto self_data = self.data_ptr<scalar_t>();
auto self_matrix_stride = matrixStride(self);
auto batch_size = batchCount(self);
auto n = self.size(-2);
auto ipiv = at::empty({n}, self.options().dtype(kInt));
auto ipiv_data = ipiv.data_ptr<int>();
int info;
// Run once, first to get the optimum work size
// Since we deal with batches of matrices with the same dimensions, doing this outside
// the loop saves (batch_size - 1) workspace queries which would provide the same result
// and (batch_size - 1) calls to allocate and deallocate workspace using at::empty()
int lwork = -1;
scalar_t wkopt;
lapackGetri<scalar_t>(n, self_data, n, ipiv_data, &wkopt, lwork, &info);
lwork = static_cast<int>(real_impl<scalar_t, value_t>(wkopt));
Tensor work = at::empty({lwork}, self.options());
auto work_data = work.data_ptr<scalar_t>();
for (int64_t i = 0; i < batch_size; i++) {
scalar_t* self_working_ptr = &self_data[i * self_matrix_stride];
lapackLu<scalar_t>(n, n, self_working_ptr, n, ipiv_data, &info);
infos[i] = info;
if (info != 0) {
return;
}
// now compute the actual inverse
lapackGetri<scalar_t>(n, self_working_ptr, n, ipiv_data, work_data, lwork, &info);
infos[i] = info;
if (info != 0) {
return;
}
}
#endif
}
Tensor _inverse_helper_cpu(const Tensor& self) {
std::vector<int64_t> infos(batchCount(self), 0);
auto self_working_copy = cloneBatchedColumnMajor(self);
AT_DISPATCH_FLOATING_AND_COMPLEX_TYPES(self.scalar_type(), "inverse_cpu", [&]{
apply_inverse<scalar_t>(self_working_copy, infos);
});
if (self.dim() > 2) {
batchCheckErrors(infos, "inverse_cpu");
} else {
singleCheckErrors(infos[0], "inverse_cpu");
}
return self_working_copy;
}
Tensor inverse(const Tensor &self) {
if (self.numel() == 0) {
return at::empty_like(self, LEGACY_CONTIGUOUS_MEMORY_FORMAT);
}
squareCheckInputs(self);
return at::_inverse_helper(self);
}
Tensor& inverse_out(Tensor &result, const Tensor &self) {
if (self.size(-1) == 0) {
return result.resize_as_(self);
}
result.copy_(native::inverse(self));
return result;
}
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ cholesky_solve ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
template<typename scalar_t>
static void apply_cholesky_solve(Tensor& b, Tensor& A, bool upper, std::vector<int64_t>& infos) {
#ifndef USE_LAPACK
AT_ERROR("cholesky_solve: LAPACK library not found in compilation");
#else
char uplo = upper ? 'U' : 'L';
auto A_data = A.data_ptr<scalar_t>();
auto b_data = b.data_ptr<scalar_t>();
auto A_mat_stride = matrixStride(A);
auto b_mat_stride = matrixStride(b);
auto batch_size = batchCount(A);
auto n = A.size(-2);
auto nrhs = b.size(-1);
int info;
for (int64_t i = 0; i < batch_size; i++) {
scalar_t* A_working_ptr = &A_data[i * A_mat_stride];
scalar_t* b_working_ptr = &b_data[i * b_mat_stride];
lapackCholeskySolve<scalar_t>(uplo, n, nrhs, A_working_ptr, n, b_working_ptr, n, &info);
infos[i] = info;
if (info != 0) {
return;
}
}
#endif
}
Tensor _cholesky_solve_helper_cpu(const Tensor& self, const Tensor& A, bool upper) {
auto self_working_copy = cloneBatchedColumnMajor(self);
auto A_working_copy = cloneBatchedColumnMajor(A);
std::vector<int64_t> infos(batchCount(self), 0);
AT_DISPATCH_FLOATING_AND_COMPLEX_TYPES(self.scalar_type(), "cholesky_solve_cpu", [&]{
apply_cholesky_solve<scalar_t>(self_working_copy, A_working_copy, upper, infos);
});
if (self.dim() > 2) {
batchCheckErrors(infos, "cholesky_solve_cpu");
} else {
singleCheckErrors(infos[0], "cholesky_solve_cpu");
}
return self_working_copy;
}
// Supports arbitrary batch dimensions for self and A
Tensor cholesky_solve(const Tensor& self, const Tensor& A, bool upper) {
TORCH_CHECK(self.dim() >= 2,
"b should have at least 2 dimensions, but has ", self.dim(), " dimensions instead");
TORCH_CHECK(A.dim() >= 2,
"u should have at least 2 dimensions, but has ", A.dim(), " dimensions instead");
Tensor self_broadcasted, A_broadcasted;
std::tie(self_broadcasted, A_broadcasted) = _linalg_broadcast_batch_dims(self, A, "cholesky_solve");
return at::_cholesky_solve_helper(self_broadcasted, A_broadcasted, upper);
}
Tensor& cholesky_solve_out(Tensor& result, const Tensor& self, const Tensor& A, bool upper) {
Tensor result_tmp;
result_tmp = at::cholesky_solve(self, A, upper);
result.resize_as_(result_tmp).copy_(result_tmp);
return result;
}
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ cholesky ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
template<typename scalar_t>
static void apply_cholesky(Tensor& self, bool upper, std::vector<int64_t>& infos) {
#ifndef USE_LAPACK
AT_ERROR("cholesky: LAPACK library not found in compilation");
#else
char uplo = upper ? 'U' : 'L';
auto self_data = self.data_ptr<scalar_t>();
auto self_matrix_stride = matrixStride(self);
auto batch_size = batchCount(self);
auto n = self.size(-2);
auto lda = std::max<int64_t>(1, n);
int info;
for (int64_t i = 0; i < batch_size; i++) {
scalar_t* self_working_ptr = &self_data[i * self_matrix_stride];
lapackCholesky<scalar_t>(uplo, n, self_working_ptr, lda, &info);
infos[i] = info;
if (info != 0) {
return;
}
}
#endif
}
Tensor _cholesky_helper_cpu(const Tensor& self, bool upper) {
std::vector<int64_t> infos(batchCount(self), 0);
auto self_working_copy = cloneBatchedColumnMajor(self);
AT_DISPATCH_FLOATING_AND_COMPLEX_TYPES(self.scalar_type(), "cholesky_cpu", [&]{
apply_cholesky<scalar_t>(self_working_copy, upper, infos);
});
if (self.dim() > 2) {
batchCheckErrors(infos, "cholesky_cpu");
} else {
singleCheckErrors(infos[0], "cholesky_cpu");
}
return self_working_copy;
}
Tensor cholesky(const Tensor &self, bool upper) {
if (self.size(-1) == 0) {
return at::empty_like(self, LEGACY_CONTIGUOUS_MEMORY_FORMAT);
}
squareCheckInputs(self);
auto raw_cholesky_output = at::_cholesky_helper(self, upper);
if (upper) {
return raw_cholesky_output.triu_();
} else {
return raw_cholesky_output.tril_();
}
}
Tensor& cholesky_out(Tensor &result, const Tensor &self, bool upper) {
if (self.size(-1) == 0) {
return result.resize_as_(self);
}
result.copy_(native::cholesky(self, upper));
return result;
}
Tensor linalg_cholesky(const Tensor &self) {
squareCheckInputs(self);
return at::_cholesky_helper(self, /*upper=*/false).tril_();
}
Tensor& linalg_cholesky_out(Tensor &result, const Tensor &self) {
TORCH_CHECK(result.scalar_type() == self.scalar_type(),
"result dtype ", result.scalar_type(), " does not match self dtype ", self.scalar_type());
Tensor result_tmp = at::linalg_cholesky(self);
at::native::resize_output(result, result_tmp.sizes());
result.copy_(result_tmp);
return result;
}
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ lu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
template<typename scalar_t>
static void apply_lu(Tensor& self, Tensor& pivots, Tensor& infos) {
#ifndef USE_LAPACK
AT_ERROR("lu: LAPACK library not found in compilation");
#else
auto self_data = self.data_ptr<scalar_t>();
auto pivots_data = pivots.data_ptr<int>();
auto infos_data = infos.data_ptr<int>();
auto self_matrix_stride = matrixStride(self);
auto pivots_matrix_stride = pivots.size(-1);
auto batch_size = batchCount(self);
auto m = self.size(-2);
auto n = self.size(-1);
for (int64_t i = 0; i < batch_size; i++) {
scalar_t* self_working_ptr = &self_data[i * self_matrix_stride];
int* pivots_working_ptr = &pivots_data[i * pivots_matrix_stride];
int* infos_working_ptr = &infos_data[i];
lapackLu<scalar_t>(m, n, self_working_ptr, m, pivots_working_ptr, infos_working_ptr);
}
#endif
}
std::tuple<Tensor, Tensor, Tensor> _lu_with_info_cpu(const Tensor& self, bool pivot, bool check_errors) {
TORCH_CHECK(pivot, "lu without pivoting is not implemented on the CPU");
TORCH_CHECK(self.dim() >= 2,
"expected tensor with 2 or more dimensions, got size: ", self.sizes(),
" instead");
auto m = self.size(-2);
auto n = self.size(-1);
auto req_size = self.sizes().vec();
req_size.pop_back();
req_size.back() = std::min(m, n);
auto pivots_tensor = at::empty(req_size, self.options().dtype(kInt));
req_size.pop_back();
auto infos_tensor = at::zeros(req_size, self.options().dtype(kInt));
Tensor self_working_copy;
if (self.numel() == 0) {
self_working_copy = at::empty_like(self, LEGACY_CONTIGUOUS_MEMORY_FORMAT);
} else {
self_working_copy = cloneBatchedColumnMajor(self);
AT_DISPATCH_FLOATING_AND_COMPLEX_TYPES(self.scalar_type(), "lu_cpu", [&]{
apply_lu<scalar_t>(self_working_copy, pivots_tensor, infos_tensor);
});
}
if (check_errors) {
if (self.dim() > 2) {
batchCheckErrors(infos_tensor, "lu", /*allow_singular=*/true);
} else {
singleCheckErrors(infos_tensor.item<int64_t>(), "lu", /*allow_singular=*/true);
}
}
return std::make_tuple(self_working_copy, pivots_tensor, infos_tensor);
}
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ triangular_solve ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
template<typename scalar_t>
static void apply_triangular_solve(Tensor& b, Tensor& A, Tensor& infos, bool upper, bool transpose, bool unitriangular) {
#ifndef USE_LAPACK
AT_ERROR("triangular_solve: LAPACK library not found in compilation");
#else
char uplo = upper ? 'U' : 'L';
char trans = transpose ? 'T' : 'N';
char diag = unitriangular ? 'U' : 'N';
auto A_data = A.data_ptr<scalar_t>();
auto b_data = b.data_ptr<scalar_t>();
auto A_mat_stride = matrixStride(A);
auto b_mat_stride = matrixStride(b);
auto batch_size = batchCount(A);
auto n = A.size(-2);
auto nrhs = b.size(-1);
auto infos_data = infos.data_ptr<int>();
for (int64_t i = 0; i < batch_size; i++) {
scalar_t* A_working_ptr = &A_data[i * A_mat_stride];
scalar_t* b_working_ptr = &b_data[i * b_mat_stride];
int* infos_working_ptr = &infos_data[i];
lapackTriangularSolve<scalar_t>(uplo, trans, diag, n, nrhs, A_working_ptr, n, b_working_ptr, n, infos_working_ptr);
}
#endif
}
std::tuple<Tensor, Tensor> _triangular_solve_helper_cpu(const Tensor& self, const Tensor& A,
bool upper, bool transpose, bool unitriangular) {
auto self_working_copy = cloneBatchedColumnMajor(self);
auto A_working_copy = cloneBatchedColumnMajor(A);
auto infos_tensor = at::empty(batchCount(self), self.options().dtype(kInt));
AT_DISPATCH_FLOATING_AND_COMPLEX_TYPES(self.scalar_type(), "triangular_solve_cpu", [&]{
apply_triangular_solve<scalar_t>(self_working_copy, A_working_copy, infos_tensor, upper, transpose, unitriangular);
});
if (self.dim() > 2) {
batchCheckErrors(infos_tensor, "triangular_solve_cpu");
} else {
singleCheckErrors(infos_tensor.item<int64_t>(), "triangular_solve_cpu");
}
return std::tuple<Tensor, Tensor>(self_working_copy, A_working_copy);
}
// Supports arbitrary batch dimensions for self and A
std::tuple<Tensor, Tensor> triangular_solve(const Tensor& self, const Tensor& A,
bool upper, bool transpose, bool unitriangular) {
TORCH_CHECK(self.dim() >= 2,
"b should have at least 2 dimensions, but has ", self.dim(), " dimensions instead");
TORCH_CHECK(A.dim() >= 2,
"u should have at least 2 dimensions, but has ", A.dim(), " dimensions instead");
Tensor self_broadcasted, A_broadcasted;
std::tie(self_broadcasted, A_broadcasted) = _linalg_broadcast_batch_dims(self, A, "triangular_solve");
return at::_triangular_solve_helper(self_broadcasted, A_broadcasted, upper, transpose, unitriangular);
}
std::tuple<Tensor&, Tensor&> triangular_solve_out(Tensor& result, Tensor& clone_A, const Tensor& self, const Tensor& A,
bool upper, bool transpose, bool unitriangular) {
Tensor result_tmp, clone_A_tmp;
std::tie(result_tmp, clone_A_tmp) = at::_triangular_solve_helper(self, A, upper, transpose, unitriangular);
result.resize_as_(result_tmp).copy_(result_tmp);
clone_A.resize_as_(clone_A_tmp).copy_(clone_A_tmp);
return std::tuple<Tensor&, Tensor&>(result, clone_A);
}
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ qr ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
template<typename scalar_t>
static void apply_geqrf(Tensor& self, Tensor& tau, int64_t m, int64_t n,
std::vector<int64_t>& infos) {
#ifndef USE_LAPACK
AT_ERROR("qr: LAPACK library not found in compilation");
#else
using value_t = typename c10::scalar_value_type<scalar_t>::type;
auto self_data = self.data_ptr<scalar_t>();
auto tau_data = tau.data_ptr<scalar_t>();
auto self_matrix_stride = matrixStride(self);
auto tau_stride = tau.size(-1);
auto batch_size = batchCount(self);
int info;
// Run once, first to get the optimum work size.
// Since we deal with batches of matrices with the same dimensions, doing this outside
// the loop saves (batch_size - 1) workspace queries which would provide the same result
// and (batch_size - 1) calls to allocate and deallocate workspace using at::empty()
int lwork = -1;
scalar_t wkopt;
lapackGeqrf<scalar_t>(m, n, self_data, m, tau_data, &wkopt, lwork, &info);
lwork = static_cast<int>(real_impl<scalar_t, value_t>(wkopt));
Tensor work = at::empty({lwork}, self.options());
for (int64_t i = 0; i < batch_size; i++) {
scalar_t* self_working_ptr = &self_data[i * self_matrix_stride];
scalar_t* tau_working_ptr = &tau_data[i * tau_stride];
// now compute the actual R and TAU
lapackGeqrf<scalar_t>(m, n, self_working_ptr, m, tau_working_ptr, work.data_ptr<scalar_t>(), lwork, &info);
infos[i] = info;
if (info != 0) {
return;
}
}
#endif
}
template<typename scalar_t>
static void apply_orgqr(Tensor& self, const Tensor& tau, int64_t m, int64_t n_columns,
int64_t k, std::vector<int64_t>& infos) {
#ifndef USE_LAPACK
AT_ERROR("qr: LAPACK library not found in compilation");
#else
using value_t = typename c10::scalar_value_type<scalar_t>::type;
auto self_data = self.data_ptr<scalar_t>();
auto tau_data = tau.data_ptr<scalar_t>();
auto self_matrix_stride = matrixStride(self);
auto tau_stride = tau.size(-1);
auto batch_size = batchCount(self);
int info;
// Run once, first to get the optimum work size.
// Since we deal with batches of matrices with the same dimensions, doing this outside
// the loop saves (batch_size - 1) workspace queries which would provide the same result
// and (batch_size - 1) calls to allocate and deallocate workspace using at::empty()
int lwork = -1;
scalar_t wkopt;
lapackOrgqr<scalar_t>(m, n_columns, k, self_data, m, tau_data, &wkopt, lwork, &info);
lwork = static_cast<int>(real_impl<scalar_t, value_t>(wkopt));
Tensor work = at::empty({lwork}, self.options());
for (int64_t i = 0; i < batch_size; i++) {
scalar_t* self_working_ptr = &self_data[i * self_matrix_stride];
scalar_t* tau_working_ptr = &tau_data[i * tau_stride];
// now compute the actual Q
lapackOrgqr<scalar_t>(m, n_columns, k, self_working_ptr, m, tau_working_ptr, work.data_ptr<scalar_t>(), lwork, &info);
infos[i] = info;
if (info != 0) {
return;
}
}
#endif
}
std::tuple<Tensor, Tensor> _linalg_qr_helper_cpu(const Tensor& self, std::string mode) {
bool compute_q, reduced;
std::tie(compute_q, reduced) = _parse_qr_mode(mode);
std::vector<int64_t> infos(batchCount(self), 0);
int64_t m = self.size(-2), n = self.size(-1);
// Setup inputs for apply_geqrf
auto self_sizes = self.sizes().vec();
self_sizes.pop_back();
self_sizes[self.dim() - 2] = std::min(m, n);
auto tau_working_copy = at::empty(self_sizes, self.options());
Tensor q_working_copy;
Tensor R;
// Setup input geometry for apply_orgqr
std::vector<int64_t> q_sizes, q_strides;
int64_t n_columns_q;
std::tie(q_sizes, q_strides, n_columns_q) = _compute_geometry_for_Q(self, reduced);
// If there are no elements, then we simply return a pair of tensors of required dimensions
if (self.numel() == 0) {
R = at::empty({n_columns_q, n}, self.options());
if (compute_q) {
int64_t n_rows_q = q_sizes[self.dim() - 2];
q_working_copy = at::eye(n_rows_q, n_columns_q, self.options());
} else {
q_working_copy = at::empty({0}, self.options());
}
return std::make_tuple(q_working_copy, R);
}
// First perform GEQRF for R and TAU (the elementary reflectors)
// We will need to generate R from the upper triangular matrix from the
// matrix input to GEQRF.
q_working_copy = at::empty_strided(q_sizes, q_strides, self.options());
q_working_copy.narrow(-1, 0, n).copy_(self);
AT_DISPATCH_FLOATING_AND_COMPLEX_TYPES(self.scalar_type(), "qr_cpu", [&]{
apply_geqrf<scalar_t>(q_working_copy, tau_working_copy, m, n, infos);
});
if (self.dim() > 2) {
batchCheckErrors(infos, "qr_cpu");
} else {
singleCheckErrors(infos[0], "qr_cpu");
}
R = q_working_copy.slice(-2, 0, n_columns_q).slice(-1, 0, n).triu();
if (!compute_q) {
// this is for mode='r'
Tensor empty_Q = at::empty({0}, self.options());
return std::make_tuple(empty_Q, R);
}
// Next perform ORGQR for Q using the results (both raw R and TAU) from GEQRF